I need to learn vocabulary words for my Spanish exam. There are 500 words and the exam grade is the percentage of these words that I recall correctly. Assuming I will recall correctly the words I learn and assuming my guesses will not yield any points, what is the least number of words I should learn to get at least $85\%$ on the exam?
Answer: Since the exam grade is the percentage of words I recall correctly, we can set up a proportion to find the minimum number of words I need to learn: \begin{align*}
\frac{\text{number of words I need to learn}}{\text{total words}}&=\frac{85\%}{100\%}\\
\frac{x}{500}&=\frac{85}{100}\\
x&=\frac{85}{100}\cdot 500\\
x&=85\cdot 5\\
x&=\boxed{425}.
\end{align*}Learning 425 words will lead to a score of exactly $85\%$, so I do not need to learn any more words than 425.